No houseruling needed (for once!). A Thief can backstrike any unaware opponent that has a strikeable back. Hiding in shadows, in many cases, takes only a round; and nobody can be aware of a hidden Thief (even more so if the party front-liners are doing their job and keeping everyone distracted). Hence, under ideal circumstances and if the dice co-operate, a Thief could backstrike every other round.
Even under that interpretation, hiding in shadows does not approach 50% until about 8th level in 1e.
A few 1e rule phrasings may induce a DM to rule the second shots do not quite work though, or are more situationally restricted.
PH page 28 "Hiding in Shadows cannot be accomplished under direct observation." so to hide you have to get fully out of direct observation.
DMG page 19 "Hide In Shadows: As is plainly stated in PLAYERS HANDBOOK, this is NEVER possible under direct
(or even indirect) observation. If the thief insists on trying, allow the attempt and throw dice, but don’t bother to read them, as the fool is as obvious as a coal pile in a ballroom. Likewise,
if a hidden thief attempts movement while under observation, the proverbial jig is up for him or her. Naturally, a creature closely pressed in melee is not likely to bother with looking for some thief not directly in the line of sight, but
if vision would normally extend to the thief’s area of activity, then observation rules apply. Unobserved attempts to hide in shadows must likewise stand the hazard of the dice roll. A score greater than the required number shows that the character’s ability is not on a par with his or her intent, and although he or she THINKS hiding has been successful, the creature looking in that direction will note a suspicious outline, form, or whatever. Note also that a thief hiding in shadows is still subject to detection just as if he or she was invisible (see INVISIBILITY, DETECTION OF INVISIBILITY table)."
So the thief needs to stay completely out of the target's vision to stay hidden in shadow, even when the target is pressed closely in melee.
PH page 27 "Back stabbing is the striking of a blow from behind, be it with club, dagger, or sword. The damage done per hit is twice normal for the weapon used per four experience levels of the thief, i.e. double damage at levels 1-4, triple at 5-8, quadruple at levels 9-12, and quintuple at levels 13-16. Note that striking by surprise from behind also increases the hit probability by 20% (+4 on the thief’s “to hit” die roll)."
Not entirely clear whether the surprise +4 to hit is just for D&D surprise and separate from the extra damage of a backstab which sounds like it is anytime from behind.
Again DMG page 19: "Back Stabbing: Opponents aware of the thief will be able to negate the attack form."
The 1e DMG rules that players are not directly privvy to says backstab is not just a matter of positioning or positioning and surprise. Awareness is sufficient to negate it.
So a judgment call on whether someone struck by the thief once is then aware of them.